A long, horizontal wire AB rests on the surface of a table and carries a current I. Horizontal wire CD is vertically above wire AB, and is free to slide up and down on the two vertical mental guides C and D (as shown in Fig) Wire CD is connected through the sliding contacts to another wire that also carries a current I, opposite in direction to the current in wire AB. The mass per unit length of the wire CD is `lambda`. To what equilibrium height h will the wire CD rise, assuming that magnetic force on it is wholly due to the current in wire AB?

Options

A. `(3mu_(0)I^(2))/(2pilambdag)`
B. `(mu_(0)I^(2))/(3pilambdag)`
C. `(5mu_(0)I^(2))/(2pilambdag)`
D. `(mu_(0)I^(2))/(2pilambdag)`

Answer

D

Explanation

Gravitational force and magnetic force are equal in magnitude and opposite in direction.
`implieslambdaLg=(mu_(0)I^(2)L)/(2pih)impliesh=(mu_(0)I^(2))/(2pilambdag)`